The Dark Sector as Truncation Decit: Dark Matter, Dark Energy, and the Cosmological Constant as Projections of Ω = 1

The standard cosmological model (ΛCDM) identies three components of the universe's energy budget: baryonic matter (≈5%), dark matter (≈27%), and dark energy (≈68%). The latter two are detected only gravitationally and remain unex- plained after ve decades of direct-detection experiments. We propose that this decomposition is not a decomposition of dierent substances but a decomposition of dierent projection operators applied to the Ω = 1 invariant. ˆ Main claim: Let ΠEM be the projection operator onto states that couple to the ˆ electromagnetic eld, and Πgrav be the projection onto states that contribute to the stress-energy tensor Tµν. Then: ˆ ρbaryon = Tr( ΠEM ˆ ˆ ˆ ˆ ˆ Πgrav |Ω⟩⟨Ω|), ρDM = Tr(( Πgrav− ΠEM Πgrav) |Ω⟩⟨Ω|), Λ = 1−Tr( Πgrav |Ω⟩⟨Ω|). Dark matter is the gravitational projection minus the electromagnetic projection. Dark energy is the residual: the part of Ω = 1 that does not project into the matter sector at all. The coincidence problemwhy ρDM/ρbaryon ≈5 and ΩΛ ≈0.68 nowdissolves: these ratios are xed by the relative sizes of the projection operators, which are structural constants of Ω, not ne-tuned parameters.